MATH 1410 - Number Concepts for Teachers

3 sem hrs cr

This course is a conceptual approach to the study of the properties of number sets within the real number system. Topics include tools for problem solving, sets, functions, logic, numeration systems, properties of and operations with whole numbers, integers, rational numbers, and real numbers. Prerequisite: Documented eligibility for collegiate mathematics; one high school credit each in algebra I, algebra II, and geometry

A minimum grade of “C” is required in this course the meet the requirement of the AST degree.

In rare and unusual circumstances, a course prerequisite can be overridden with the permission of the Department Lead for the discipline.

Formerly/Same As (Formerly MAT 1230)

Transfer (UT) or Non-Transfer Course (UN): UT

By the end of the course, students will be able to…

• give the student who is choosing to become a teacher in the elementary grades a comprehensive review of the basic laws and relationships of fundamental elementary school mathematics.
• promote the development of teaching strategies appropriate to grade level and required mathematical development.
• promote an understanding and appreciation for the National Council of Teachers of Mathematics “Curriculum and Evaluations Standards for School Mathematics” for grades K-4 and grades 5-8.

Course Objectives

Throughout the course, students will have the opportunity to…

• explain, illustrate, and use Polya’s 4-step problem-solving process: understand the problem, devise a plan, carry out the plan, look back.
• explain, illustrate, and apply the following strategies: make a drawing, guess and check, make a table, use a model, work backward, use a variable, make an organized list, and eliminate possibilities.
• apply concepts of patterns to problem solving: Fibonacci numbers, Pascal’s triangle, arithmetic sequence, geometric sequence, triangular numbers, and finite differences.
• use algorithms for solving equations and inequalities in problem solving.
• use concepts of set theory in problem solving: disjoint sets, subsets, equal sets, one-to-one correspondence, finite sets, infinite sets, intersection of sets, union of sets, complement of a set, and Venn diagrams.
• use concepts of functions and graphs in problem solving.
• apply concepts of deductive reasoning to problem solving.
• represent numeric values using symbolisms of a variety of numeration systems: Egyptian, Roman, Mayan, and Hindu-Arabic.
• illustrate and apply models for numeration and place value in bases two through twelve.
• apply models for addition and subtraction algorithms.
• apply techniques for mental calculations: compatible numbers, substitutions, equal differences, and add-up method.
• apply techniques for estimation of sums and differences: rounding, compatible numbers, and front-end estimation.
• apply models for multiplication algorithms.
• apply techniques of mental multiplication: compatible numbers, substitutions, and equal products.
• apply techniques for estimation of products: rounding, compatible numbers, and front-end estimation.
• apply models for division algorithms.
• apply the technique of equal quotients for mental division.
• apply techniques for estimation of quotients: rounding, compatible numbers, and front-end estimation.
• apply concepts of exponents.
• apply concepts of number theory to problem solving: factors, multiples, divisibility, prime and composite numbers.
• apply concepts of greatest common divisor (factor) and least common multiple in problem solving.
• apply models for operations with integers.
• apply models for concepts of fractions: part-to-whole, division, and ratio.
• apply concepts of fraction relationships: equality, common denominators, inequality, density, mixed numbers, and improper fractions.
• apply algorithms for operations with fractions: addition, subtraction, multiplication, and division.
• apply concepts for mental calculations with fractions: compatible numbers, substitutions, equal differences, add-up, and equal quotients.
• apply concepts for estimation with fractions: rounding and compatible numbers.
• use concepts of fractions in problem solving.
• apply models for decimal concepts: decimal squares and number line.
• apply concepts of decimal relationships: equality and inequality.
• apply concepts of rational numbers: decimal form, density, and estimation.
• apply algorithms for operations with decimals: addition, subtraction, multiplication, and division.
• convert repeating decimals to rational numbers.
• apply concepts for mental computation with decimals: substitutions and add-up, equal quotients, and compatible numbers.
• apply concepts for estimation with decimals: rounding, front-end estimation, and compatible numbers.
• use concepts of ratio, percent, and scientific notation in problem solving.